A sample of 99 distances has a mean of 24 feet and a median of 21.5 feet. Unfortunately, it has just been discovered that an observation which was erroneously recorded as "30" actually had a
value of "35". If we make this correction to the data, what would happen to the mean and median?
A. The median remains the same, but the mean is increased.
B. The mean remains the same, but the median is increased.
C. The mean and median are both increased.
D. The mean and median remain the same.

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step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)

  b.   the average rate of change of f(x) is less than the average rate of change of g(x).

step-by-step explanation:

since the length of the interval is the same in each case, we only need to compare the change in y-value to see which is greater.

so the change in y-value for function f is (6 )) = 9.

the table tells us

so the change in y-value for function g is (31 -1) = 30.

the change in y-value of f(x) on the interval is less than the change in y-value of g(x) on the same interval, so the average rate of change of f(x) is less than the average rate of change of g(x).

f(x) = y

f(-3) = -5

step-by-step explanation: